Accurate modelling of flow induced stresses in rigid colloidal aggregates

A method has been developed to estimate the motion and the internal stresses induced by a fluid flow on a rigid aggregate. The approach couples Stokesian dynamics and structural mechanics in order to take into account accurately the effect of the complex geometry of the aggregates on hydrodynamic forces and the internal redistribution of stresses. The intrinsic error of the method, due to the low-order truncation of the multipole expansion of the Stokes solution, has been assessed by comparison with the analytical solution for the case of a doublet in a shear flow. In addition, it has been shown that the error becomes smaller as the number of primary particles in the aggregate increases and hence it is expected to be negligible for realistic reproductions of large aggregates. The evaluation of internal forces is performed by an adaptation of the matrix methods of structural mechanics to the geometric features of the aggregates and to the particular stress-strain relationship that occurs at intermonomer contacts. A preliminary investigation on the stress distribution in rigid aggregates and their mode of breakup has been performed by studying the response to an elongational flow of both realistic reproductions of colloidal aggregates (made of several hundreds monomers) and highly simplified structures. A very different behaviour has been evidenced between low-density aggregates with isostatic or weakly hyperstatic structures and compact aggregates with highly hyperstatic configuration. In low-density clusters breakup is caused directly by the failure of the most stressed intermonomer contact, which is typically located in the inner region of the aggregate and hence originates the birth of fragments of similar size. On the contrary, breakup of compact and highly cross-linked clusters is seldom caused by the failure of a single bond. When this happens, it proceeds through the removal of a tiny fragment from the external part of the structure. More commonly, however, breakup takes place through a sequence of bond failures that start at the periphery of the aggregates and then moves toward the interior according to a crack propagation mechanism. A gradual transition between these two modes of breakup has been found as the density of the aggregates increases.